The family of a woman found dead on Wellington's Mt Victoria yesterday are struggling to come to grips with what has happened, police say.

Detective Inspector Paul Basham said the body of a 38-year-old woman found by a group of joggers had been identified, but her name would not be released until more family members were notified.

"Understandably, they are still struggling to come to grips with what has happened, and our thoughts are with them at this very difficult time," Basham said.

Police last night recovered the body, after it was found off a running track near Alexandra Park, above Wellington Girls' East College.

A post-mortem examination had begun earlier today and was still ongoing, he said.

"Until such time as the post-mortem has been completed, police aren't able to comment on the possible cause of death.

"At this early stage we are still treating the death as 'unexplained' and are keeping an open mind to a number of possible scenarios," Basham said.

Police were continuing a scene examination, a post mortem examination and interviews with a number of people who had come forward with information.

A 25-year-old man arrested in the area yesterday for obstruction was spoken to but later released.

"We are still however keen to hear from anyone who was in the Alexandra Park / Mt Victoria town belt area around 11am yesterday, or who may have other relevant information to please come forward. This will assist us in piecing together her final movements and provide a clearer picture of what may have led to her death."

Yesterday Basham would not say how far off the track the woman's body was found but described the terrain as rugged. The body did not appear to have been there long but he would not comment on her clothing or whether she was fully dressed.

Former Wellington East principal Janice Campbell said she felt the track was a bad idea when it was built about 10 years ago. The school fenced off the track and planted "nasty things" to deter pupils from entering the area as it was unsafe.

"You've got all sorts of perverts up there."

Acting Wellington East principal Ann Greenaway said there had been few problems since the area was fenced off, although staff were aware the track was not school property.

The school would wait for the result of the police investigation before deciding what to tell the pupils, she said.

"It's something we're always a bit worried about because it's still a public track."

Wellington College headmaster Roger Moses was in Melbourne when contacted yesterday and had not heard about the discovery.

Some pupils used the pathways but to the best of his knowledge there had never been any problems in the area.

"Over the years there's been the odd vagrant that's hung around the top there...but it's kind of separate from the school so I don't know much about it, but it's a shocker."